Dynamic behavior of a fractional order prey-predator model with group defense

Alidousti, Javad; Ghafari, Elham

doi:10.1016/j.chaos.2020.109688

Cited by 47 publications

(25 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The fractional-order models are also well-liked due to their capability in providing an exact description of different nonlinear phenomena [32]. In recent years, the development of fractional-order models grows rapidly and becomes popular in studying the dynamical behavior of predator-prey interaction [17,[33][34][35][36][37][38]. It has been shown that the order of the fractional derivate significantly affects the dynamical behavior of the models, which is in contrast to the first-order derivative models that depend only on the values of parameters.…”

Section: Variables and Parameters Description X(t)mentioning

confidence: 99%

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

Panigoro

Suryanto

Kusumawinahyu

et al. 2020

Axioms

View full text Add to dashboard Cite

The harvesting management is developed to protect the biological resources from over-exploitation such as harvesting and trapping. In this article, we consider a predator–prey interaction that follows the fractional-order Rosenzweig–MacArthur model where the predator is harvested obeying a threshold harvesting policy (THP). The THP is applied to maintain the existence of the population in the prey–predator mechanism. We first consider the Rosenzweig–MacArthur model using the Caputo fractional-order derivative (that is, the operator with the power-law kernel) and perform some dynamical analysis such as the existence and uniqueness, non-negativity, boundedness, local stability, global stability, and the existence of Hopf bifurcation. We then reconsider the same model involving the Atangana–Baleanu fractional derivative with the Mittag–Leffler kernel in the Caputo sense (ABC). The existence and uniqueness of the solution of the model with ABC operator are established. We also explore the dynamics of the model with both fractional derivative operators numerically and confirm the theoretical findings. In particular, it is shown that models with both Caputo operator and ABC operator undergo a Hopf bifurcation that can be controlled by the conversion rate of consumed prey into the predator birth rate or by the order of fractional derivative. However, the bifurcation point of the model with the Caputo operator is different from that of the model with the ABC operator.

show abstract

Section: Variables and Parameters Description X(t)mentioning

confidence: 99%

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

Panigoro

Suryanto

Kusumawinahyu

et al. 2020

Axioms

View full text Add to dashboard Cite

show abstract

“…Kemudian pada tahun 1934, Gause mengembangkan model Lotka-Voltera [4], pada model Gause tersebut laju pertumbuhan prey diasumsikan bertumbuh secara logistik dan pertumbuhan predator bertumbuh secara eksponensial [5]. Kajian tentang model predator-prey merupakan hal yang sangat menarik sehingga sampai saat ini masih terus dipelajari dan dikembangkan seperti di [6][7][8][9][10][11][12][13].…”

Section: Pendahuluanunclassified

Analisis Kestabilan Model Predator-Prey dengan Infeksi Penyakit pada Prey dan Pemanenan Proporsional pada Predator

Maisaroh

Resmawan

Rahmi

2020

Jambura J. Biomath.

View full text Add to dashboard Cite

The dynamics of predator-prey model with infectious disease in prey and harvesting in predator is studied. Prey is divided into two compartments i.e the susceptible prey and the infected prey. This model has five equilibrium points namely the all population extinction point, the infected prey and predator extinction point, the infected prey extinction point, and the co-existence point. We show that all population extinction point is a saddle point and therefore this condition will never be attained, while the other equilibrium points are conditionally stable. In the end, to support analytical results, the numerical simulations are given by using the fourth-order Runge-Kutta method.

show abstract

“…During the past few decades, a great deal of valuable research fruits on dynamical behavior of the above four-type predator-prey models has been covered. For example, Alidousti and Ghafari [3] investigated the Hopf bifurcation and limit cycle of the fractional-order predator-prey model; Sasmal and Takeuchi [4] studied the stability behavior of all equilibria, bifurcation nature, global features, and multistability of a predator-prey model; Ryu and Ko [5] discussed the asymptotic peculiarity for positive solutions for a prey-predator model; Guo et al [6] proved the appearance of traveling waves in a prey-predator system. Zhang et al [7] revealed the effect of the fear factor on the periodic solution of a prey-predator model.…”

Section: Introductionmentioning

confidence: 99%

“…where t 0 > 0 is a constant. e key object of this work focuses on existence, uniqueness, nonnegativity, stability, and bifurcation phenomenon of model (3). Different from the methodology in [26,27], in this paper, we will mainly discuss the various dynamics by applying fractional-order differential equation theory.…”

Section: Introductionmentioning

confidence: 99%

Further Study on Dynamics for a Fractional‐Order Competitor‐Competitor‐Mutualist Lotka–Volterra System

Tang

2021

Complexity

View full text Add to dashboard Cite

On the basis of the previous publications, a new fractional-order prey-predator model is set up. Firstly, we discuss the existence, uniqueness, and nonnegativity for the involved fractional-order prey-predator model. Secondly, by analyzing the characteristic equation of the considered fractional-order Lotka–Volterra model and regarding the delay as bifurcation variable, we set up a new sufficient criterion to guarantee the stability behavior and the appearance of Hopf bifurcation for the addressed fractional-order Lotka–Volterra system. Thirdly, we perform the computer simulations with Matlab software to substantiate the rationalisation of the analysis conclusions. The obtained results play an important role in maintaining the balance of population in natural world.

show abstract

Dynamic behavior of a fractional order prey-predator model with group defense

Cited by 47 publications

References 25 publications

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

Analisis Kestabilan Model Predator-Prey dengan Infeksi Penyakit pada Prey dan Pemanenan Proporsional pada Predator

Further Study on Dynamics for a Fractional‐Order Competitor‐Competitor‐Mutualist Lotka–Volterra System

Contact Info

Product

Resources

About